Unit 5

Area and Geometric Measurement:  Volume

Grade 5




Students will find the volume of a rectangular prism by counting unit cubes.  Students will practice measuring volume using cubic centimeters, cubic inches, cubic feet, and other units.  Work will also involve applying the formulas V = l x w x h and V = b x h.  

Students will select appropriate units, strategies, and tools for solving real word problems involving estimating and measuring volume.




Major Clusters

NF – Number and Operations - Fractions

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.


Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

  1. Construct a model to develop understanding of the concept of multiplying two fractions and create a story context for the equation.  [in general, (m/n)  (c/d) = (mc) / (nd).]


Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Measurement and Data

Geometric measurement:  understand concepts of volume and relate volume to multiplication and to addition


Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

a.    A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.

b.    A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.


Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.


Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

a.    Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

b.    Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

c.       Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.



Enduring Understandings:


·         Volume is represented in cubic units.

·         Volume can be expressed in both customary and metric units.

·         A square unit could have fractional lengths.  As long as the lengths of a square unit are the same, it is still considered a square unit.


Essential Questions:


·         How do I use the language of math to make sense of/solve a problem?

·         How can the volume of cubes and rectangular prisms be found?

·         What is the relationship among the volumes of geometric solids?

·         Why is volume represented with cubic units and area represented with square units?

·         How do you find volume using fractional lengths?